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Re: Functions with parameters?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg22252] Re: [mg22214] Functions with parameters?
*From*: BobHanlon at aol.com
*Date*: Sat, 19 Feb 2000 01:33:55 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
f[x_, a_] := Log[x/(x - a)]
Off[Plot3D::gval]; Off[Power::infy]; Off[Plot3D::plnc];
The function will have a discontinuity (i.e., not be defined) when x = a.
Plot3D[Abs[f[x, a]], {x, -5, 5}, {a, -5, 5}, PlotPoints -> 20];
Plot3D[Re[f[x, a]], {x, -5, 5}, {a, -5, 5}, PlotPoints -> 20];
Plot3D[Im[f[x, a]], {x, -5, 5}, {a, -5, 5}, PlotPoints -> 20];
For the function to have real values, the argument of the Log must be positive
Needs["Algebra`InequalitySolve`"]
InequalitySolve[x/(x - a) > 0, {x, a}]
x < 0 && a > x || x > 0 && a < x
Since you also specified that a is positive
InequalitySolve[x/(x - a) > 0 && a > 0, {x, a}]
x < 0 && a > 0 || x > 0 && 0 < a < x
Plot3D[f[x, a], {x, -5, 5}, {a, 0, 5}, PlotPoints -> 20];
For the derivative
g[x_, a_] := Evaluate[D[f[x, a], x] // Simplify // Factor]
g[x, a]
a/((a - x)*x)
The derivative has discontinuities at x = 0 and x = a. Draw the graphs as
above for g[x, a].
Bob Hanlon
In a message dated 2/18/2000 4:02:56 AM, tautenhahn at fichtelgebirge.org writes:
>I have Mathematica 4 and I want to discuss a simple function with a
>parameter; The problem, however, is that I neither found some help in
>the online help of Mathematica nor in the book (which is about
>Mathematica 3) by Michael Kofler.
>I don't know if it is possible to do everything I want to do with
>Mathematica and that's why I'm asking here.
>The function I want to discuss is
>
>f(x)=ln(x/(x-a) with a>0
>ok, in Mathematica you type f[x_]=Log[x/(x-a)].
>what I want to do is:
>
>* where is this function defined (I don't know if this is the right
>English word; for example 1/x is *not* defined for x=0; i hope you
>understand what I mean);
>
>* derivatives etc. --> no problem, but again: where is f'(x) defined?
>
>* Plot the function for several values of a
>
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